L-fuzzy normal spaces and Tietze extension theorem (Q1101989)

In this excellent note it is shown that an L-fuzzy topological space X is normal [in the sense of \textit{B. Hutton}, J. Math. Anal. Appl. 50, 74-79 (1975; Zbl 0297.54003)] iff for any pair of functions h,g: \(X\to {\mathbb{R}}(L)\) such that \(g\leq h\) (g is upper semicontinuous and h is lower semicontinuous) there exists a continuous function \(f: X\to {\mathbb{R}}(L)\) such that \(g\leq f\leq h\). This characterization of the normal L-fuzzy topological spaces is used to prove a fuzzy topological version of Tieze's classical theorem which provide an affirmative answer to a question of \textit{S. E. Rodabaugh} [Fuzzy Sets Syst. 11, 163-183 (1983; Zbl 0525.54002)].